Mathematics for Computer Sciences II
by R. Okazaki
2004 Spring Term
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This course is an introduction to the language of sets.
Its primary goal is a grasp of the basic notions related with sets,
functions and relations.
Its secondary goal is a touch at the very basic notions related with
mathematical structure.
After successfully learning basics from this course,
students will be familier to mathematical conception in computer sciences.
Plan
04/09 Sets as Extension
04/16 Logic and Sets
04/23 Inclusion of Sets
05/07 Basic Operations of Sets
05/14 Law of Operattions of Sets
05/21 Operation and Inclusion of Sets
05/28 Direct Product of Sets
06/04 Graph and Relation
06/11 Order as Relation
06/18 Equivalence Relation
06/25 Function as Special Relation
07/02 Operations of Functions
07/09 Mathematical Structure
Evaluation
Examination 100%
Through examination, achievement in several points will be verified:
understanding of concrete sets;
understanding of sets through diagram;
logical treatment of sets from description of elements;
ablility to perform calculation of sets;
some ability of inference in problems formulated with sets;
basic knowledge of functions, relations and structure.
How to Study
Students can touch the basic notions of sets, functions and relations
through rich material presented at the course.
Students can acquire the ability to understand and/or express
notions of
discrete mathematics through diagrams,
that are used everywhere in the course.
Students can become familier to sets because
daily subjects will be often used as material.
Students can learn a basic view point of mathematics and computer sciences
because
recovery of
properties of aggregate objects
from
information of individual objects
will be repeatedly practiced in the course.